Question: What is the coefficient of $x^4$ in the expansion of $(1-2x^2)^5$?
Solution: Using the binomial theorem, we find that the $x^4=(x^2)^2$ term of the expansion is $\binom{5}{2}(1)^3(-2x^2)^2=10(4x^4)=40x^4$.  Thus, the desired coefficient is $\boxed{40}$.